Monopolistic competition and oligopoly

# Conflict between individual incentive and joint

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Conflict between individual incentive and joint incentives

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Most games do not have dominant strategies. In this case, identify strategies that are strictly dominated by other strategies. Players are strictly better off playing strategies other than dominated one. Using rationality and common knowledge, we can eliminate dominated strategy and by iteration, we reach an equilibrium pair of strategies.
Player 2 Player 1 L C R T 1, 1 2, 0 2, 2 M 0, 3 1, 5 4, 4 B 2, 4 3, 6 3, 0

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Some games can not be solved even with iterated dominance. Then we use the concept of Nash equilibrium: A combination of players’ best response strategies. If player 1 does his best by playing strategy a, when player 2 plays strategy b, and similarly if player 2 does his best by playing strategy b against player 1’s play of strategy a, then the pair of strategies (a,b) is a Nash equilibrium.
Player 2 Player 1 L C R T 2, 1 2, 2 0, 3 M 1, 1 1, 1 1, 1 B 0, 1 0, 0 2, 2

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Contrary to Dominant or Dominated strategies, Nash equilibrium solution concept almost always produces an equilibrium. There may be problem of multiple equilibria In this class of games, we observe: Players want to coordinate More than one point of coordination Main disagreement is on which point to coordinate.
Wife Husband Cricket Movie Cricket 6,2 0, 0 Movie 0, 0 2, 6 Two Nash Equilibria: (Cricket, Cricket) and (Movie, Movie)

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Player 2 L R Player 1 U 4, 0 0, 1 D 0, 1 1, 0
Sometime Nash equilibrium does not exist in pure strategies. A mixed strategy of a player in a strategic game is a probability distribution over the player’s actions. The goal of a mixed strategy is to make your opponent indifferent between two options in a 2X2 game.

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Player 2 chooses p and (1-p) such that Player 1 is indifferent between U and D Player 1 chooses q and (1-q) such that Player 2 is indifferent between L and R Player 2 L (p) R (1-p) Player 1 U (q) 4, 0 0, 1 D (1-q) 0, 1 1, 0
Player B Player A Head Tail Head 1,-1 -1,1 Tail -1,1 1,-1

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Games where one player moves after another player.
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• Spring '12
• AbhinavDhar
• Game Theory, Airbus, player, low price

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